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Persistent Friedel oscillations in Graphene due to a weak magnetic field
Mesoscale and Nanoscale Physics · Submitted 27 Jul 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Here we show that a weak uniform magnetic field affects the Friedel oscillations in an anomalous way.
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The abstract, sentence by sentence
Two opposite chiralities of Dirac electrons in a 2D graphene sheet modify the Friedel oscillations strongly: electrostatic potential around an impurity in graphene decays much faster than in 2D electron gas. At distances $r$ much larger than the de Broglie wavelength, it decays as $1/r^3$. Here we show that a weak uniform magnetic field affects the Friedel oscillations in an anomalous way. It creates a field-dependent contribution which is {\em dominant} in a parametrically large spatial interval $p_0^{-1}\lesssim r\lesssim k_Fl^2$, where $l$ is the magnetic length, $k_F$ is Fermi momentum and $p_0^{-1}=(k_Fl)^{4/3}/k_F$. Moreover, in this interval, the field-dependent oscillations do not decay with distance. The effect originates from a spin-dependent magnetic phase accumulated by the electron propagator. The obtained phase may give rise to novel interaction effects in transport and thermodynamic characteristics of graphene and graphene-based heterostructures.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Two opposite chiralities of Dirac electrons in a 2D graphene sheet modify the Friedel oscillations strongly: electrostatic potential around an impurity in graphene decays much faster than in 2D electron gas. | background 0.92 | 0.24 | 0.07 | asserted 1.00 |
| s1 | At distances $r$ much larger than the de Broglie wavelength, it decays as $1/r^3$. | background 0.78 | 0.42 | 0.04 | asserted 1.00 |
| s2 | Here we show that a weak uniform magnetic field affects the Friedel oscillations in an anomalous way. | contribution 0.75 | 0.83 | 0.25 | asserted 1.00 |
| s3 | It creates a field-dependent contribution which is {\em dominant} in a parametrically large spatial interval $p_0^{-1}\lesssim r\lesssim k_Fl^2$, where $l$ is the magnetic length, $k_F$ is Fermi momentum and $p_0^{-1}=(k_Fl)^{4/3}/k_F$. | result 0.98 | 0.91 | 0.62 | asserted 1.00 |
| s4 | Moreover, in this interval, the field-dependent oscillations do not decay with distance. | result 1.00 | 0.91 | 0.40 | asserted 1.00 |
| s5 | The effect originates from a spin-dependent magnetic phase accumulated by the electron propagator. | interpretation 0.92 | 0.77 | 0.06 | asserted 1.00 |
| s6 | The obtained phase may give rise to novel interaction effects in transport and thermodynamic characteristics of graphene and graphene-based heterostructures. | interpretation 0.99 | 0.43 | 0.10 | hedged possibility 1.00 |
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Original abstract
Two opposite chiralities of Dirac electrons in a 2D graphene sheet modify the Friedel oscillations strongly: electrostatic potential around an impurity in graphene decays much faster than in 2D electron gas. At distances $r$ much larger than the de Broglie wavelength, it decays as $1/r^3$. Here we show that a weak uniform magnetic field affects the Friedel oscillations in an anomalous way. It creates a field-dependent contribution which is {\em dominant} in a parametrically large spatial interval $p_0^{-1}\lesssim r\lesssim k_Fl^2$, where $l$ is the magnetic length, $k_F$ is Fermi momentum and $p_0^{-1}=(k_Fl)^{4/3}/k_F$. Moreover, in this interval, the field-dependent oscillations do not decay with distance. The effect originates from a spin-dependent magnetic phase accumulated by the electron propagator. The obtained phase may give rise to novel interaction effects in transport and thermodynamic characteristics of graphene and graphene-based heterostructures.
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Cites as background 1 paper
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Unique electronic properties of Graphene [ref] stem from the fact that it is single-atom-thick.
Deformation of graphene sheet: Interaction of fermions with phonons · introduction · 0.90
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